Blow-up result for a weakly coupled system of two Euler-Poisson-Darboux-Tricomi equations with time derivative nonlinearity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917764371841024 |
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| author | Hassen, Mohamed Fahmi Ben Hamouda, Makram Hamza, Mohamed Ali |
| author_facet | Hassen, Mohamed Fahmi Ben Hamouda, Makram Hamza, Mohamed Ali |
| contents | We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms. The latter are specifically of great interest from both physical and mathematical points of view since they allow the speeds of propagation to be time-dependent ones. However, we assume in this work that both waves are propagating with the same speeds. Employing this fact together with other hypotheses on the aforementioned parameters (mass and damping coefficients), we obtain a new blow-up region for the system under consideration, and we show a lifespan estimate of the maximal existence time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Blow-up result for a weakly coupled system of two Euler-Poisson-Darboux-Tricomi equations with time derivative nonlinearity Hassen, Mohamed Fahmi Ben Hamouda, Makram Hamza, Mohamed Ali Analysis of PDEs 35L05, 35L71, 35B44 We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms. The latter are specifically of great interest from both physical and mathematical points of view since they allow the speeds of propagation to be time-dependent ones. However, we assume in this work that both waves are propagating with the same speeds. Employing this fact together with other hypotheses on the aforementioned parameters (mass and damping coefficients), we obtain a new blow-up region for the system under consideration, and we show a lifespan estimate of the maximal existence time. |
| title | Blow-up result for a weakly coupled system of two Euler-Poisson-Darboux-Tricomi equations with time derivative nonlinearity |
| topic | Analysis of PDEs 35L05, 35L71, 35B44 |
| url | https://arxiv.org/abs/2306.14768 |